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1. Calculate Refractive Index ($\mu$):
$\mu = \frac{c}{v} = \frac{3 \times 10^8}{2 \times 10^8} = 1.5$.
2. Determine Radius of Curvature ($R$):
For a lens with radius of aperture $r = 3 \text{ cm}$ and thickness $t = 0.3 \text{ cm}$, the radius of curvature is given by $R \approx \frac{r^2}{2t}$ (for small thickness).
$R = \frac{3^2}{2 \times 0.3} = \frac{9}{0.6} = 15 \text{ cm}$.
3. Lens Maker's Formula:
$\frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$. For a plano-convex lens, $R_1 = R$ and $R_2 = \infty$.
$\frac{1}{f} = (1.5 - 1) \left( \frac{1}{15} \right) = 0.5 \times \frac{1}{15} = \frac{1}{30}$.
Thus, $f = 30 \text{ cm}$.
A particle of mass $m$ is projected with speed $v$ at $45°$ to the horizontal. When it returns to ground level, the magnitude of the change in momentum is:
Initial vertical component: $v_y = v\sin45° = \dfrac{v}{\sqrt{2}}$ (upward)
On landing (by symmetry): $v_y' = \dfrac{v}{\sqrt{2}}$ (downward)
Horizontal component unchanged. Change in momentum:
$|\Delta\vec{p}| = m\left|\Delta v_y\right| = m\cdot\dfrac{2v}{\sqrt{2}} = \mathbf{mv\sqrt{2}}$
Management by Objectives (MBO) was introduced by Peter Drucker in his 1954 book The Practice of Management. MBO is a process where:
- Managers and employees jointly set specific, measurable objectives
- Performance is evaluated against these pre-set objectives
- Feedback and appraisal are systematic
In nursing management, MBO helps Head Nurses set clear performance targets for nursing staff, improving accountability and service quality. Other options: Frederick Taylor — Scientific Management; Maslow — Hierarchy of Needs; McGregor — Theory X and Y.
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